It’s a common enough refrain: we see a film or a work of art that grabs hold of our emotions, and we say it totally absorbed us. But in the art of Park McArthur, absorption is much more than a metaphor. The young American sculptor, whose newest exhibition opens this week at the Chisenhale gallery in east London, is renowned in the US for her hushed, politically engaged, often deeply moving exhibitions, making use of unorthodox materials. Her art is absorbing; the art is absorbent, too.

Her three new series of works, all made for this first UK solo show, display a fascination with stuff that slurps in fluids or holds back bodies. Expanses of acoustic foam, made of high-density polyurethane, segment the Chisenhale and suck in sound. Among these sound-absorbing sculptures are large, blank sheets of custom-made paper.

“These larger pieces of paper have a super-absorbent polymer, like what you find inside diapers,” she tells me over breakfast in New York. The sheets are huge now, she says, but you should have seen them while they were still hydrated. “They dry to an inch and a half thick, which means they were even thicker before ... Before all of the liquid had been dried or squeezed out, five staff members had to carry them through.”

If the acoustic form absorbs sound and the polymer-based papers absorb liquid, a third component of the show has its own role to play. On low-slung steel trays, McArthur has arranged masses of condoms, as if someone is about to have a very fun night. “I was thinking about the appearance of condom bowls, and about their genealogy. Take one. Or take however many you want! Plunge your hand in!”

Bowls of condoms, especially in the grim first years of Aids, were as much a political statement as a combat for public health. “You can compare them to flyers,” she says, “papers distributed with a specific message or demand.”

They are not the only ribbed, lubricated barriers on display. McArthur’s collection of single-use latex items also includes gloves, dental dams, finger condoms, and other stretchy prophylactics. It sounds like a sexy show. “Could be,” she says. “I don’t really know if it’ll be sexy or not.”

But the erotic does interest her. “Audre Lorde wrote a wonderful essay called The Uses of the Erotic, and one of its main ideas is that when we only relate to people in processes of exchange, when we divorce things from their deeper aspects, we’re robbed of those relationships’ erotic power. So, sexy but also erotic: those things have a nice friction to them.”

McArthur was born in 1984 in North Carolina. She still has a hint of a southern twang, but her conversation is all New York guilelessness. She trained as a painter before turning to sculpture, and her art wrestles with how sculpture exploded from its old dependable forms – a marble or bronze object on a plinth, usually – and became just about anything.

The foam in her work is a commercially available readymade, bought wholesale, and continues a tradition that began with Marcel Duchamp and extends past minimalism. The paper, by contrast, is painstakingly crafted by artisans. The condoms and dental dams, heaped into uncountable bundles, recall the freely distributed posters and candies of Cuban-American artist Félix González-Torres: “They’re readymade materials, but open for the taking.”

Just as González-Torres recoded the stacks and piles of minimal sculpture into searing memorials for people with Aids, McArthur, too, has found a way to infuse seemingly blank materials with fraught subjects: in her case, disability. In her astounding exhibition Ramps, seen at the New York gallery Essex Street in 2014, a grid of nearly two dozen gently inclined blocks at first seemed to be a riff on floor-based minimalist sculpture by the likes of Donald Judd. They were in fact temporary access ramps, used by McArthur to enter or exit buildings.

“I was thinking about how ramps appear in the construction spaces on sidewalks,” she tells me. “And also about where curb cuts appear, and how they sometimes require you to back up or reroute. That doubling back – the taking up of time – opens up another route. There’s always another set of possibilities when you double back.”

The UK helped to shape her ideas on this issue. “Think about the social model of disability – the idea that the built environment and the policy or judicial world are the source of disablement or disability, rather than an individual impairment,” she says. “That idea came out of British disability rights and community spheres. So the invitation to do a show in Britain was an invitation to think more about being the beneficiary of those ideas.” Disability culture in the UK, she says, is really vibrant.

Britain was also a pioneer in providing care to disabled people outside institutions – establishing the Independent Living Fund (ILF) in 1988, several years before the US equivalent, the Americans With Disabilities Act. Both of these landmarks acts were adopted by conservative governments: Margaret Thatcher’s and George HW Bush’s respectively. “In the US it was an anti-discrimination act based in individual rights,” says McArthur, “so that disabled Americans could enter the workforce and not receive welfare benefits. A shrinking of the welfare state.” The ILF closed in 2015, with disability benefits now administered by local authorities.

How a person or a person’s body can be formed or deformed through political and social forces is a question that haunts McArthur’s sculpture, and that she wrestles with in her own life. “I’m 31. The Reagan-Bush-Thatcher lineage, and the rise of neoliberalism, is something my generation can map on to our own existence in the world. British friends and friends of friends have told me about Disabled People Against Cuts. But can we even have the imagination to think of something that would be better than what the ILF provided? Can we only insist on these things not being cut? It’s hard for us to imagine something that would meet even more needs. I want to know what that feels like. And it feels pretty dire.”

Since the advent of modernism, and its bold but suspicious claims to speak in a universal language, many artists outside the dominant representation – women, artists of colour, queer artists, and indeed artists with disabilities – have had to negotiate a tricky terrain. To what degree is any artwork independent of an artist’s biography? Can any of us escape from the straitjacket of who we are, and how we’re classified?

“Actually, it’s a joyful problem,” says McArthur. “Artists have always wanted to keep slippery ... Is this artwork about this or about that? It’s always much more complicated than either one of those things.”